Skip to main content

Minimum Area Rectangle II

Problem Statement​

You are given an array of points in the X-Y plane points where points[i] = [xi, yi].

Return the minimum area of any rectangle formed from these points, with sides not necessarily parallel to the X and Y axes. If there is not any such rectangle, return 0.

Answers within 10-5 of the actual answer will be accepted.

Leetcode link

Example 1:​

ex1

Input: points = [[1,2],[2,1],[1,0],[0,1]]
Output: 2.00000
Explanation: The minimum area rectangle occurs at [1,2],[2,1],[1,0],[0,1], with an area of 2.

Example 2:​

ex2

Input: points = [[0,1],[2,1],[1,1],[1,0],[2,0]]
Output: 1.00000
Explanation: The minimum area rectangle occurs at [1,0],[1,1],[2,1],[2,0], with an area of 1.

Example 3:​

ex3

Input: points = [[0,3],[1,2],[3,1],[1,3],[2,1]]
Output: 0
Explanation: There is no possible rectangle to form from these points.

Constraints:​

  • 1 <= points.length <= 500
  • points[i].length == 2
  • 0 <= xi, yi <= 4 * 104
  • All the given points are unique.

Code​

Python Code
class Solution:
    def minAreaFreeRect(self, points):
        mn, st, n = float('inf'), {(x, y) for x, y in points}, len(points)
        for i in range(n):
            x1, y1 = points[i]
            for j in range(i + 1, n):
                x2, y2 = points[j]
                for k in range(j + 1, n):
                    x3, y3 = points[k]
                    if not (x3 - x1) * (x2 - x1) + (y3 - y1) * (y2 - y1) and (x3 + (x2 - x1), y3 + (y2 - y1)) in st:
                        mn = min(mn, ((x2 - x1) ** 2 + (y2 - y1) ** 2) ** 0.5 * ((x3 - x1) ** 2 + (y3 - y1) ** 2) ** 0.5)
        return mn if mn < float("inf") else 0